Washington's Mathieu Perreault made it 1-0 by poking in the rebound of Green's shot at 11:18 of the first period. Brooks Laich made it 2-0 five minutes later.
Marian Hossa cut the Blackhawks' deficit in half less than a minute later when he knocked in his own rebound during a power play.
Chicago's Peter LeBlanc received a match penalty for a hit to the head of Capitals forward Alexander Semin at 12:37 of the third period. A slashing penalty on Hossa gave the Caps a 5-on-3 advantage, and Green beat Crawford with just over 3 minutes to play.